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Mensa Brain Juggling 2007/08 - Round 5

Just have a look at these three watches with a strange hands position :

Assuming we know that it is 2 o'clock on the left and 3 o'clock in the middle - what time do we have on the right then?

26. A Series of Numbers

1 10 120 141 164 299 226 255 386 329 ...

What are the next three numbers in this series?

27. Belligerent Queens

As so often before : the grownup-version of a Junior Brain Juggling puzzle :

...

...

Put as many white and black queens as possible on this 8*8 chessboard, without a white queen being able to capture a black one and vice versa. Queens of the same colour of course do not hurt each other.

ATTENTION : The number of black and white queens may differ by only 1 !

(A queen can move vertically, horizontally or diagonally. It therefore can capture queens in the same row, column or diagonal.)

28. Plutoku

In the year 2121 a small human expedition lands on the (dwarf)planet Pluto for the very first time.

(The humans are all Mensans of course (who else would people want to send to Pluto?). And, naturally, one of them is you (who else ... but we had that already).)

To their big surprise, they meet intelligent life there. To their even BIGGER surprise, the Plutonians turn out to be more intelligent than the Mensans and capture them with patience and a snare.

Finally, the Mensans succeed in making themselves understood, and the Plutonians are willing to release them. But under one condition only : they must help the Plutonians solve an ancient riddle of the past.

The Mensans discuss for a while and finally agree. The Plutonians drag a big and heavy stone slab towards them :

If the Earthlings can tell them which characters are missing on the empty squares, they shall be free again!

The Mensans are stunned! After careful examination they come to the conclusion that yes, even the old Plutonians did play SUDOKU!

But will the Mensans be able to help the young Plutonians find the solution?

Of course you know the rules. But bear in mind : the Plutonians only accept Plutonian characters as a solution!

29. Round Table

You are invited to join a big Mensa festivity of the Truth Lovers (always saying the truth) and the Liars (always lying). As usual on such occasions, you of course want to find out who is who. All the guests are sitting around a big, round table. You incidentally bow down to one of them and ask him, who is sitting beside him.

As you have a very loud and sonorous voice, everybody can hear you. As usual among Mensans, everybody feels concerned and wants to say something.

"TWO LIARS!!!" you hear from everywhere around.

Dazed and stunned from the loudness, you stagger backwards a little. "How ... how many of you are there, actually?" you ask shyly.

"Ain't true, we are 100!" a child sitting a little further away shouts.

Who of the two is telling the truth (assuming one of them does)?

30. Paint It Black

To awake the sleeping artist inside you, you are hereby forced to paint a beautiful picture :

All squares in this 30*30 picture are either black or white. How many squares in every row or column are black is shown by the numbers on the left and above the picture.

What do these numbers mean? For instance : the 11th row : (2,4,3,3). It means : in this row we first have a block of 2 black squares, then a block of 4, then 3 and then again 3. Inbetween them, there is always at least one or more white squares. Also, before the first and after the last block of black squares, there can be one or more white squares.

Apply that to every row and column in your picture and the pleasant illuminating should be only a matter of technique. :-)